Lunch spot in Chelsea near 24th and 7th
You can enter the High Line from 20th and 10th Ave.
If you stay near 24th St and walk west to 9th Avenue, you can go to:
Cookshop - really good brunch, reserve beforehand on OpenTable to minimize wait time
Grand Sichuan - some of the best spicy Chinese food in town
Co aka Company - Jim Lahey of Sullivan St Bakery's pizzeria, Naples inspired but not traditional
Some good suggestions near you in this recent thread: http://chowhound.chow.com/topics/737146
Also Rickshaw Dumplings, 23 between 5 and 6
Haven't been there yet, but there's a new Chock Full O'Nuts on 23 at 5th (may be more of interest to us old natives.....)
While the weather is nice, there's the original Shake Shack in Madison Park (23 at 5).
Good dry barbeque at RUB, 23 at 7.
And so on....
Rickshaw Dumpling Bar
61 W 23rd St, New York, NY 10010